According to the U.S. Census Bureau, the county has a total area of 1,090 square miles (2,800 km2), of which 881 square miles (2,280 km2) is land and 209 square miles (540 km2) (19%) is water.[4] It borders the Gulf of Mexico. Baffin Bay makes up a large part of the border with Kenedy County.

There were 10,896 households out of which 34.90% had children under the age of 18 living with them, 52.10% were married couples living together, 13.90% had a female householder with no husband present, and 29.50% were non-families. 22.30% of all households were made up of individuals and 7.60% had someone living alone who was 65 years of age or older. The average household size was 2.78 and the average family size was 3.30.

In the county, the population was spread out with 27.30% under the age of 18, 15.70% from 18 to 24, 27.40% from 25 to 44, 19.00% from 45 to 64, and 10.60% who were 65 years of age or older. The median age was 29 years. For every 100 females, there were 101.00 males. For every 100 females age 18 and over, there were 98.50 males.

The median income for a household in the county was $29,313, and the median income for a family was $33,055. Males had a median income of $31,179 versus $19,494 for females. The per capita income for the county was $13,542. About 21.20% of families and 26.70% of the population were below the poverty line, including 35.50% of those under age 18 and 15.60% of those age 65 or over.

Kleberg county is named after Robert Justus Kleberg Sr. (1803–1888), a Prussian settler, was born on September 10, 1803, in Herstelle, Westphalia.
His father was a merchant. Kleberg was educated in the classics and attended the University of Göttingen, where he received a J.D. degree. After graduating he was appointed a justice of assizes. He married Rosalie von Roeder near Paderborn, Prussia, in ...1834.
They emigrated to Texas that year and settled in Cat Spring in 1836. In the Republic of Texas, Kleberg was associate commissioner and president of the Board of Land Commissioners (1837–38), justice of the peace (1841), and chief justice of Austin County (1846). In 1847 the Kleberg’s moved to Meyersville, where Kleberg was elected county commissioner in 1848 and chief justice in 1853.
Kleberg fought in the battle of San Jacinto in Capt. Moseley Baker's company and subsequently served as one of the Texas guards for Gen. Santa Anna. After the revolution, he volunteered for six months' duty in the Texas army in a campaign against the Indians on Escondido Creek.
Kleberg supported the cause of the Confederacy. When the Civil War broke out he raised a company of militia but because of his advanced age was not received into active service. Robert and Rosa raised their own seven children in addition to several young Roeder relatives. Their youngest son, Robert Justus Kleberg Jr. married Alice Gertrudis King.
Kleberg died on October 23, 1888, near Cuero and was buried there. His grave is marked by a monument in the form of a soldier's tent with the words "Remember the Alamo" carved at the base. Kleberg County was named in his honor in 1913; a marker at his home site near Cuero was erected in 1936.